Question

In the following exercises, simplify the equation $5q^3\left(q^2\hspace{0.17em}-\hspace{0.17em}2q\hspace{0.17em}+\hspace{0.17em}6\right)$.

Short answer

The simplified expression is $5q^5-10q^4+30q^3$.

Step-by-step solution

Step 1. Given Information.

The expression is $5q^3\left(q^2\hspace{0.17em}-\hspace{0.17em}2q\hspace{0.17em}+\hspace{0.17em}6\right)$.

Step 2. Simplify given equation.

Simplifying $5q^3\left(q^2\hspace{0.17em}-\hspace{0.17em}2q\hspace{0.17em}+\hspace{0.17em}6\right)$

Apply distributive rule, we get:-

$$\begin{gathered} 5q^3\left(q^2\hspace{0.17em}-\hspace{0.17em}2q\hspace{0.17em}+\hspace{0.17em}6\right)=5q^3{q}^2+5q^3\left(-2q\right)+5q^3·\hspace{0.17em}6 \\ 5q^3{q}^2+5q^3\left(-2q\right)+5q^3·\hspace{0.17em}6=5q^5-10q^4+30q^3 \end{gathered}$$